Experimental design principles for isotopically instationary 13C labeling experiments

13C metabolic flux analysis (MFA) is a well-established tool in Metabolic Engineering that found numerous applications in recent years. However, one strong limitation of the current method is the requirement of an-at least approximate-isotopic stationary state at sampling time. This requirement leads to a principle lower limit for the duration of a 13C labeling experiment. A new methodological development is based on repeated sampling during the instationary transient of the 13C labeling dynamics. The statistical and computational treatment of such instationary experiments is a completely new terrain. The computational effort is very high because large differential equations have to be solved and, moreover, the intracellular pool sizes play a significant role. For this reason, the present contribution works out principles and strategies for the experimental design of instationary experiments based on a simple example network. Hereby, the potential of isotopically instationary experiments is investigated in detail. Various statistical results on instationary flux identifiability are presented and possible pitfalls of experimental design are discussed. Finally, a framework for almost optimal experimental design of isotopically instationary experiments is proposed which provides a practical guideline for the analysis of large-scale networks.     

Kinetic and thermodynamic principles determining the structural design of ATP-producing systems

It is theoretically analysed whether the structural design of ATP-producing pathways, in particular the design of glycolysis, may be explained by optimization principles. On the basis of kinetic and thermodynamic principles conclusions are derived concerning the stoichiometry of these pathways in states of high ATP production rates. One of the extensions to previous investigations is that the concentrations of the adenine nucleotides are taken into account as variable quantities. This necessitates the consideration of an interaction of the ATP-producing system I with an external ATP-consuming system II. A great variety of pathways is studied which differ in the number and location of ATP-consuming reactions, ATP-producing reactions and reactions involving inorganic phosphate. The corresponding number of possible pathways may be calculated in an explicit manner as a function of the number of those reactions which do not couple to ATP or inorganic phosphate. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations and all rate equations are expressed in terms of equilibrium constants and characteristic times. A thermodynamical analysis of the two coupled systems yields upper and lower limits for the concentration of ATP and an explicit expression for the maximal difference between the number of ATP-producing and ATP-consuming reactions of system I. The following results of the optimization are obtained. (i) The ATP production rate always increases if the ATP-producing reactions as well as those reactions characterized by an uptake of inorganic phosphate are shifted as far as possible towards the end of system I. (ii) Explicit conditions for the optimal location of the ATP-consuming reactions are presented. The results are discussed in the context of characteristic times as well as in terms of enzyme kinetic parameters. (iii) For two sets of characteristic times the resulting stoichiometries and their corresponding steady-state fluxes are investigated in detail. One of these stoichiometries shows a close correspondence to contemporary standard glycolysis. (iv) It is shown that most possible pathways result in a very low steady-state flux, that is, the optimal stoichiometry is characterized by a significant selective advantage. (v) The standard free energy profile of a pathway with an optimal stoichiometry is discussed. It differs significantly from the free energy profiles of nonoptimized pathways.     

Toward predicting metabolic fluxes in metabolically engineered strains

Predicting metabolic fluxes of a genetically engineered organism is an important step toward rational pathway design. However, because of various regulatory mechanisms, which are complex, often ill-characterized, and sometimes undiscovered, predicting metabolic fluxes using kinetic simulation is difficult. We propose to incorporate regulatory constraints in flux calculation to allow prediction of the steady-state fluxes without complete kinetics. The regulatory constraint, in its linear form, is derived from the dynamic metabolic control theory and involves the flux control coefficients. It is shown that with these constraints, the responses to metabolic perturbation can be predicted. Conversely, the regulatory constraints and the control coefficients can be determined by comparing the experimental data with the prediction. Therefore, this approach may offer a practical direction toward prediction of fluxes for metabolically engineered organisms.     

Pathway analysis, engineering, and physiological considerations for redirecting central metabolism

The rate and yield of producing a metabolite is ultimately limited by the ability to channel metabolic fluxes from central metabolism to the desired biosynthesis pathway. Redirection of central metabolism thus is essential to high-efficiency production of biochemicals. This task begins with pathway analysis, which considers only the stoichiometry of the reaction networks but not the regulatory mechanisms. An approach extended from convex analysis is used to determine the basic reaction modes, which allows the determination of optimal and suboptimal flux distributions, yield, and the dispensable sets of reactions. Genes responsible for reactions in the same dispensable set can be deleted simultaneously. This analysis serves as an initial guideline for pathway engineering. Using this analysis, we successfully constructed an Escherichia coli strain that can channel the metabolic flow from carbohydrate to the aromatic pathway with theoretical yield. This analysis also predicts a novel cycle involving phosphoenolpyruvate (PEP) carboxykinase (Pck) and the glyoxylate shunt, which can substitute the tricarboxylic acid cycle with only slightly less efficiency. However, the full cycle could not be confirmed in vivo, possibly because of the regulatory mechanism not considered in the pathway analysis.In addition to the kinetic regulation, we have obtained evidence suggesting that central metabolites are involved in specific regulons in E. coli. Overexpression of PEP-forming enzymes (phosphoenolpyruvate synthase [Pps] and Pck) stimulates the glucose consumption rate, represses the heat shock response, and negatively regulates the Ntr regulon. These results suggest that some glycolytic intermediates may serve as a signal in the regulation of the phosphotransferase system, heat shock response, and nitrogen regulation. However, the role of central metabolites in these regulations has not been determined conclusively. (c) 1996 John Wiley & Sons, Inc.     

Development of a metabolic network design and optimization framework incorporating implementation constraints: a succinate production case study

We have developed a pathway design and optimization scheme that accommodates genetically and/or environmentally derived operational constraints. We express the full set of theoretically optimal pathways in terms of the underlying elementary flux modes and then examine the sensitivity of the optimal yield to a wide class of physiological perturbations. Though the scheme is general it is best appreciated in a concrete context: we here take succinate production as our model system. The scheme produces novel pathway designs and leads to the construction of optimal succinate production pathway networks. The model predictions compare very favorably with experimental observations.     

Towards a rational approach to the optimization of flux in microbial biotransformations

Many historical attempts to increase the yield of biotechnological processes have been at best semi-empirical. However, given the availability of modern techniques of genetic and protein engineering, the question arises as to how one might rationally seek to choose the most suitable genes to clone and/or modify for this purpose. The metabolic control theory of Kaeser, Burns, Heinrich and Rapoport allows one to decide quantitatively which enzymatic steps are (most) rate-determining to the flux through desired pathways (and why). An extension of these principles allows one rationally to identify optimal strategies for the improvement of microbial processes.     

Is maximization of molar yield in metabolic networks favoured by evolution?

Stoichiometric analysis of metabolic networks allows the calculation of possible metabolic flux distributions in the absence of kinetic data. In order to predict which of the possible fluxes are present under certain conditions, additional constraints and optimization principles can be applied. One approach of calculating unknown fluxes (frequently called flux balance analysis) is based on the optimality principle of maximizing the molar yield of biotransformations. Here, the relevance and applicability of that approach are examined, and it is compared with the principle of maximizing pathway flux. We discuss diverse experimental evidence showing that, often, those biochemical pathways are operative that allow fast but low-yield synthesis of important products, such as fermentation in Saccharomyces cerevisiae and several other yeast species. Together with arguments based on evolutionary game theory, this leads us to the conclusion that maximization of molar yield is by no means a universal principle.     

Time hierarchy in enzymatic reaction chains resulting from optimality principles

Several optimality principles reasonable for the evolution of enzyme reaction chains are formulated, considering the kinetic parameters of the enzymes to be variables. The solutions of these parametric programming problems are studied for the case of linear kinetics and turn out to be not unique in every case. The investigations are confined to stationary states. The net flux through the chain is considered a fixed parameter. The optimality criteria concern the osmotic pressure caused by the intermediates, various relaxation times, largest time scale, and controllability. They all yield distinct time hierarchies. The influence of a constraint concerning the sum of intermediate concentrations is studied. Various combinations of the single criteria are treated as multiobjective programming problems.     

黄色短杆菌TK0303的L-亮氨酸生物合成途径分析

应用途径分析方法分析了在拟稳态时黄色短杆菌(Brevibacterium flavum)TK0303由葡萄糖发酵生产L-亮氨酸的代谢途径,确定了L-亮氨酸合成的最佳途径和最大理论产率。通过比较途径分析所获得的反应模型,确定了丙酮酸和乙酰辅酶A是L-亮氨酸合成途径的关键节点。在此基础上改变外界环境因子,强化L-亮氨酸生物合成途径中丙酮酸和乙酰辅酶A两个关键节点的代谢流,以期进一步提高L-亮氨酸产率。结果表明,经过谷氨酸以及醋酸铵的调节,代谢途径流量发生显著变化,L-亮氨酸产量有明显提高。     

Genome-scale in silico aided metabolic analysis and flux comparisons of Escherichia coli to improve succinate production

In the post-genome era, it is one challenge to understand the cellular metabolism at the systematic levels. Mathematical modeling of microorganisms and subsequent computer simulation are effective tools for systems biology. In this paper, based on the genome-scale Escherichia coli stoichiometric model iJR904, through the GAMS linear programming package, the in silico maximal succinate yield was estimated to be 1.714 mol/mol glucose. When another two constraints were added, the maximal succinate yield dropped to 1.60 mol/mol glucose. Further analysis substantiated the uniqueness of the flux distribution under such constraints. After comparisons with the metabolic flux analysis (MFA) results computed from the wet experimental data of the three kinds of E. coli, three potential improvement target sites, the glucose phosphotransferase transport system, the pyruvate carboxylase, and the glyoxylate shunt, were identified and selected for the genetic modifications. All the three genetic modified strains showed increased succinate yield. The final strain TUQ19/pQZ6 had a high yield of 1.29 mol succinate/mol glucose and high productivity. The success of the above experiments proved that this in silico optimal succinate production pathway is reasonable and practical. This method may also be used as a general strategy to help enhance the yields of other favorable metabolites in E. coli.     

Metabolic pathway analysis for rational design of L-methionine production by Escherichia coli and Corynebacterium glutamicum

Metabolic pathway analysis was carried out to predict the metabolic potential of Corynebacterium glutamicum and Escherichia coli for the production of L-methionine. Based on detailed stoichiometric models for these organisms, this allowed the calculation of the theoretically optimal methionine yield and related metabolic fluxes for various scenarios involving different mutants and process conditions. The theoretical optimal methionine yield on the substrates glucose, sulfate and ammonia for the wildtype of C. glutamicum is 0.49 (C-mol) (C-mol)(-1), whereas the E. coli wildtype exhibits an even higher potential of 0.52 (C-mol) (C-mol)(-1). Both strains showed completely different optimal flux distributions. C. glutamicum has a high flux through the pentose phosphate pathway (PPP), whereas the TCA cycle flux is very low. Additionally, it recruits a metabolic cycle, which involves 2-oxoglutarate and glutamate. In contrast, E. coli does minimize the flux through the PPP, and the flux through the TCA cycle is high. The improved potential of the E. coli wildtype is due to its membrane-bound transhydrogenase and its glycine cleavage system as shown by additional simulations with theoretical mutants. A key point for maximizing methionine yield is the choice of the sulfur source. Replacing sulfate by thiosulfate or sulfide increased the maximal theoretical yield in C. glutamicum up to 0.68 (C-mol) (C-mol)(-1). A further increase is possible by the application of additional C1 sources. The highest theoretical potential was obtained for C. glutamicum applying methanethiol as combined source for C1 carbon and sulfur (0.91 (C-mol) (C-mol)(-1)). Substrate requirement for maintenance purposes reduces theoretical methionine yields. In the case of sulfide used as sulfur source a maintenance requirement of 9.2 mmol ATP g(-1) h(-1), as was observed under stress conditions, would reduce the maximum theoretical yield from 67.8% to 47% at a methionine production rate of 0.65 mmol g(-1) h(-1). The enormous capability of both organisms encourages the development of biotechnological methionine production, whereby the use of metabolic pathway analysis, as shown, provides valuable advice for future strategies in strain and process improvement.     

Therapeutic siRNA: principles, challenges, and strategies

RNA interference (RNAi) is a remarkable endogenous regulatory pathway that can bring about sequence-specific gene silencing. If harnessed effectively, RNAi could result in a potent targeted therapeutic modality with applications ranging from viral diseases to cancer. The major barrier to realizing the full medicinal potential of RNAi is the difficulty of delivering effector molecules, such as small interfering RNAs (siRNAs), in vivo. An effective delivery strategy for siRNAs must address limitations that include poor stability and non-targeted biodistribution, while protecting against the stimulation of an undesirable innate immune response. The design of such a system requires rigorous understanding of all mechanisms involved. This article reviews the mechanistic principles of RNA interference, its potential, the greatest challenges for use in biomedical applications, and some of the work that has been done toward engineering delivery systems that overcome some of the hurdles facing siRNA-based therapeutics.     

Kinetic modelling of plant metabolic pathways

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.     

Analysis of operating principles with S-system models

Operating principles address general questions regarding the response dynamics of biological systems as we observe or hypothesize them, in comparison to a priori equally valid alternatives. In analogy to design principles, the question arises: Why are some operating strategies encountered more frequently than others and in what sense might they be superior? It is at this point impossible to study operation principles in complete generality, but the work here discusses the important situation where a biological system must shift operation from its normal steady state to a new steady state. This situation is quite common and includes many stress responses. We present two distinct methods for determining different solutions to this task of achieving a new target steady state. Both methods utilize the property of S-system models within Biochemical Systems Theory (BST) that steady states can be explicitly represented as systems of linear algebraic equations. The first method uses matrix inversion, a pseudo-inverse, or regression to characterize the entire admissible solution space. Operations on the basis of the solution space permit modest alterations of the transients toward the target steady state. The second method uses standard or mixed integer linear programming to determine admissible solutions that satisfy criteria of functional effectiveness, which are specified beforehand. As an illustration, we use both methods to characterize alternative response patterns of yeast subjected to heat stress, and compare them with observations from the literature.     

Coping with complexity: machine learning optimization of cell-free protein synthesis

Biological systems contain complex metabolic pathways with many nonlinearities and synergies that make them difficult to predict from first principles. Protein synthesis is a canonical example of such a pathway. Here we show how cell-free protein synthesis may be improved through a series of iterated high-throughput experiments guided by a machine-learning algorithm implementing a form of evolutionary design of experiments (Evo-DoE). The algorithm predicts fruitful experiments from statistical models of the previous experimental results, combined with stochastic exploration of the experimental space. The desired experimental response, or evolutionary fitness, was defined as the yield of the target product, and new experimental conditions were discovered to have ～ 350% greater yield than the standard. An analysis of the best experimental conditions discovered indicates that there are two distinct classes of kinetics, thus showing how our evolutionary design of experiments is capable of significant innovation, as well as gradual improvement.     

Assessing the impact of substrate-level enzyme regulations limiting ethanol titer in Clostridium thermocellum using a core kinetic model

Clostridium thermocellum is a promising candidate for consolidated bioprocessing because it can directly ferment cellulose to ethanol. Despite significant efforts, achieved yields and titers fall below industrially relevant targets. This implies that there still exist unknown enzymatic, regulatory, and/or possibly thermodynamic bottlenecks that can throttle back metabolic flow. By (i) elucidating internal metabolic fluxes in wild-type C. thermocellum grown on cellobiose via ¹³C-metabolic flux analysis (¹³C-MFA), (ii) parameterizing a core kinetic model, and (iii) subsequently deploying an ensemble-docking workflow for discovering substrate-level regulations, this paper aims to reveal some of these factors and expand our knowledgebase governing C. thermocellum metabolism. Generated ¹³C labeling data were used with ¹³C-MFA to generate a wild-type flux distribution for the metabolic network. Notably, flux elucidation through MFA alluded to serine generation via the mercaptopyruvate pathway. Using the elucidated flux distributions in conjunction with batch fermentation process yield data for various mutant strains, we constructed a kinetic model of C. thermocellum core metabolism (i.e. k-ctherm138). Subsequently, we used the parameterized kinetic model to explore the effect of removing substrate-level regulations on ethanol yield and titer. Upon exploring all possible simultaneous (up to four) regulation removals we identified combinations that lead to many-fold model predicted improvement in ethanol titer. In addition, by coupling a systematic method for identifying putative competitive inhibitory mechanisms using K-FIT kinetic parameterization with the ensemble-docking workflow, we flagged 67 putative substrate-level inhibition mechanisms across central carbon metabolism supported by both kinetic formalism and docking analysis.     

Optimal stoichiometric designs of ATP-producing systems as determined by an evolutionary algorithm.

The design of metabolic pathways is thought to be the result of an optimization process such that the structure of contemporary metabolic routes maximizes a particular objective function. Recently, it has been shown that some essential stoichiometric properties of glycolysis can be explained on the basis of the requirement for a high ATP production rate. Because the number of stoichiometrically feasible designs increases strongly with the number of reactions involved, a systematic analysis of all the possibilities turns out to be inaccessible beyond a certain system size. We present, therefore, an alternative approach to compute in a more efficient way the optimal design of glycolysis interacting with an external ATP-consuming reaction. The algorithm is based on the laws of evolution by natural selection, and may be viewed as a particular version of evolutionary algorithms. The following conclusions are derived: (a) evolutionary algorithms are very useful search strategies in determining optimal stoichiometries of metabolic pathways. (b) Essential topological features of the glycolytic network may be explained on the basis of flux optimization. (c) There is a strong interrelation between the optimal stoichiometries and the thermodynamic and kinetic properties of the participating reactions. (d) Some subsequences of reactions in optimal pathways are strongly conserved at variation of system parameters, which may be understood by applying principles of metabolic control analysis.     

The influence of metabolic network structures and energy requirements on xanthan gum yields

The metabolic network of Xanthomonas campestris is complex since a number of cyclic pathways are present making simple stoichiometric yield predictions difficult. The influence of certain pathway configurations and the resulting variations in flux have been examined as regards the maximum yield potential of this bacteria for xanthan gum production. These predictions have been compared with experimental results showing that the strain employed is functioning close to its theoretical maximum as regards yield criteria. The major constraint imposed on the network concerns energy availability which has a more pronounced effect on yield than carbon precursor supply. This can be attributed to the relatively high maintenance requirements determined experimentally and incorporated into the model. While some of this overall energy burden will undoubtedly be associated with incompressible metabolic requirements such as sugar uptake and xanthan efflux mechanisms, future strain improvement strategies will need to attack other non-essential energy-consuming reactions, if yields are to be further increased.     

Metabolic control analysis under uncertainty: framework development and case studies

Information about the enzyme kinetics in a metabolic network will enable understanding of the function of the network and quantitative prediction of the network responses to genetic and environmental perturbations. Despite recent advances in experimental techniques, such information is limited and existing experimental data show extensive variation and they are based on in vitro experiments. In this article, we present a computational framework based on the well-established (log)linear formalism of metabolic control analysis. The framework employs a Monte Carlo sampling procedure to simulate the uncertainty in the kinetic data and applies statistical tools for the identification of the rate-limiting steps in metabolic networks. We applied the proposed framework to a branched biosynthetic pathway and the yeast glycolysis pathway. Analysis of the results allowed us to interpret and predict the responses of metabolic networks to genetic and environmental changes, and to gain insights on how uncertainty in the kinetic mechanisms and kinetic parameters propagate into the uncertainty in predicting network responses. Some of the practical applications of the proposed approach include the identification of drug targets for metabolic diseases and the guidance for design strategies in metabolic engineering for the purposeful manipulation of the metabolism of industrial organisms.